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Question

If $n left parenthesis A right parenthesis$ denotes the number of elements in the set $A$ and if $n open parentheses A close parentheses equals 4 comma blank n open parentheses B close parentheses equals 5$ and $n open parentheses A intersection B close parentheses equals 3$ , then $n left square bracket left parenthesis A cross times B right parenthesis intersection left parenthesis B cross times A right parenthesis right square bracket$ is equal to

(a) 8
9
10
11

The correct answer is: 9

Given, $n open parentheses A close parentheses equals 4 comma blank n open parentheses B close parentheses equals 5$ and $n open parentheses A intersection B close parentheses equals 3$
$therefore n open square brackets open parentheses A cross times B close parentheses intersection open parentheses B cross times A close parentheses close square brackets equals 3 to the power of 2 end exponent equals 9$

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